已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值

已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值
已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值

已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值
∵x(x-1)-(x²-y)=-3
∴x²-x-x²+y=-3
∴x-y=3
∴2xy-x²+3-y²
=-(x²-2x+y²)+3
=-(x-y)²+3
=-(3)²+3
=-9+3
=-6

x(x-1)-(x²-y)=-3
x²-x-x²+y=-3
x-y=3

2xy-x²+3-y²=-(x²+y²-2xy)+3
=-(x-y)²+3
=-3²+3
=-6

由于y-x=-3，故原式=3-（x-y）²=3-9=-6.